Journal of Electrical Engineering
www.jee.ro
Firefly Algorithm based Optimal Power Flow for Sizing of Thyristor Controlled
Series Capacitor to enhance line based voltage stability
Venkateswara Rao Bathina1, Venkata Nagesh Kumar Gundavarapu 2
1
Department of Electrical and Electronics, GITAM University, Visakhapatnam, Andhra Pradesh, INDIA
Department of Electrical and Electronics, GITAM University, Visakhapatnam, Andhra Pradesh, INDIA
vraobathina@yahoo.in, gundavarapu_kumar@yahoo.com
2
Abstract. Reactive Power compensation in transmission
systems improves the stability of the system and also
reduces the transmission line losses. Installing Flexible
AC Transmission System (FACTS) devices are the
effective means to control reactive power compensation.
However, due to the high cost of FACTS devices, it is
important to optimally place these controllers in the
system. Out of the different FACTS devices, TCSC is the
most effective device for series compensation. This paper
presents a Sensitivity analysis based Complex Power
Flow Sensitivity Index (CPSI) proposed for placing the
TCSC at an appropriate location. Once the location to
install TCSC is identified, the optimal sizing of TCSC is
determined through Firefly Algorithm based multicriterion objective function comprising of four objectives
minimize total real power loss, minimize total voltage
magnitude deviations, minimize the fuel cost of total real
power generation and minimize the branch loading to
obtain the optimal power flow. Simulations have been
carried out in MATLAB environment for the IEEE 14-bus
system, the IEEE 30-bus system and IEEE57 bus system.
The results have been taken for Firefly Algorithm based
Optimal Power Flow without and with TCSC. The results
obtained with Firefly Algorithm were compared with
Genetic Algorithm (GA). The results indicate that FA is
an easy to use and better optimization technique
compared with GA.
Keywords
Firefly Algorithm, Optimal placement, Sensitivity
index, TCSC.
1. Introduction
Power systems are becoming increasingly more
complex due to the interconnection of regional system
and deregulation of the overall electricity market [1, 2]. It
has become essential to better utilize the existing power
networks to increase capacities by installing Flexible AC
Transmission System (FACTS) controllers. The variables
and parameter of the transmission line, which include line
reactance, voltage magnitude, and phase angle are able to
be controlled using FACTS controllers in a fast and
effective way. The benefits derived from FACTS
controllers include improvement of the stability of power
system networks, such as voltage stability, line stability,
small signal stability, transient stability, enhance power
transfer capability and thus enhance system reliability.
However, controlling power flows is the main function of
FACTS [3-6].
Out of the several preventive and corrective
measures suggested in literature to protect power system
networks against voltage collapse, the placement of
FACTS controllers has been established as an effective
means. However, due to high cost of the FACTS devices,
it is important to optimally place these controllers in the
system. The Thyristor Controlled Series Capacitor
(TCSC) is one of the most effective Flexible AC
Transmission System devices [7-10]. It offers fast-acting
reactive power compensation on high-voltage electricity
transmission networks with much faster response
compared to the traditional control devices [11].
This paper presents Sensitivity analysis based
Complex Power Flow Sensitivity Index (CPSI) proposed
for placing the TCSC at appropriate location. A new Meta
heuristic optimization technique called Firefly Algorithm
is introduced to find the optimal size of TCSC device to
improve line stability. Its performance is compared with
Genetic Algorithm (GA) [12-17] technique. The real and
reactive power generation values and voltage limits for
generator buses are taken as constraints, along with
reactance limits of the TCSC, during the optimization.
Computer simulations using MATLAB were done for the
IEEE14 bus system, the IEEE 30 bus system and the
IEEE57 bus system. In this paper, a new line-based
voltage stability index is implemented to evaluate the line
stability condition in a power system.
2. Problem Formulation
In this paper, the multi objective function is formulated to
find optimal sizing of TCSC device by minimizing
certain objective functions subject to satisfying some
network constraints. The multi-objective problem can be
written mathematically as follows.
1
Journal of Electrical Engineering
www.jee.ro
Sk is the apparent power in line k and S kmax is the
maximum apparent power in line k.
2.1. Objective function
For a given system load, the best configuration of TCSC
device is obtained by minimizing the objective function:
5) Equality constraints:
N
Min F = min⁡(W1 ∗ FC + W2 ∗ FPloss + W3 ∗ FVD
+ W4 ∗ FS
(1)
Where W1, W2, W3, W4 are the weighting factors
W1 + W2 + W3 + W4 = 1
PGi =
i=1
PDi + PL
N
N
Q Gi =
Reactance of TCSC has been added as a control variable
along with real power generation of the generator buses
for optimization problem. TCSC limits are given as:
min
X TCSC
≤ X TCSC ≤ X max
TCSC
(2)
1) Fuel cost:
The objective function considering the minimization of
total generation cost can be represented by following
quadratic equation
ng
ai PGi2 + bi PGi + ci
(3)
i=1
i=1
Q Di + Q L
8
i=1
Where i=1,2,3,.......,Nbus and Nbus = no. of. buses
PL is total active power losses
QL is total reactive power losses
6) Inequality constraints:
Generator bus Voltage limits:
min
max
VGi
≤ VGi ≤ VGi
(9)
Where i=1,2,3,.......,Nbus and Nbus = no.of. buses
Real power generation limit:
PGimin ≤ PGi ≤ PGimax
Where ng = no. of generator buses
(7)
i=1
Where i=1,2,3,.......,Nbus and Nbus = no. of. Buses
W1 = W2 = W3 = W4 = 0.25
FC = min
N
(10)
Where i=1,2,3,......,ng and ng= no.of.generator buses
a, b, c are the fuel cost coefficients of a generator unit
Reactive Powergeneration limits:
2) Active Power Loss:
The objective of this function is to minimize real power
losses in the transmission lines. It can be expressed as
ntl
real (Sijk + Sjik )
FPLoss = min
(4)
k=1
Where ntl=no. Of transmission lines
Sij is the total complex power flow of line i – j
3) Voltage Deviation:
To have a good voltage performance, the voltage
deviation at each bus must be made as small as possible.
The Voltage Deviation (VD) can be expressed as:
Nbus
⋮ Vk − Vkref ⋮2
FVD = min
max
Qmin
Gi ≤ Q Gi ≤ Q Gi
(11)
2.2. Fast Voltage Stability Index (FVSI)
Several techniques were proposed to analyse the static
voltage stability condition in a system. Some of them
were utilized the voltage stability indices referred either
to a bus or to a line as an indicator to voltage collapse. In
this paper, a new line-based voltage stability index is
proposed to evaluate the line stability condition in a
power system. This index is called as Fast Voltage
Stability Index (FVSI). The system becomes unstable if
FVSI is equal to or greater than unity.
FVSI can be expressed as
5
FVSIij =
k=1
Vk is the voltage magnitude at bus k
4 Z2 Qj
Vi2 X
12
Where Z is the line impedance
Vkref is the reference voltage magnitude at bus k
X is the line reactance
4) Branch loading:
Qj is the reactive power at bus j (receiving end bus)
The objective of minimizing the branch loading in the
transmission lines is to enhance the security level of the
system. It can be expressed as
ntl
FS = min S = min
k=1
⋮ Sk ⋮
( max )2
⋮ Sk
⋮
(6)
Vi is the voltage magnitude at bus i (sending end bus)
Any line in the system that exhibits FVSI close to unity
indicate that the line is may lead to system violation.
Therefore, FVSI has to be maintained less than unity in
order to maintain a stable system.
2
Journal of Electrical Engineering
www.jee.ro
3.
Thyristor
controlled
capacitor (TCSC)
series
The basic Thyristor-controlled series capacitor scheme
proposed in 1986 by Vithaythil with others is a method of
“rapid adjustment of network impedance”. Apart from
controlling the line power transfer capability, TCSC also
enhances system stability [18-21]. The basic module of
the TCSC is shown in Fig. 1. It consists of a series
compensating capacitor shunted by thyristor controlled
reactor [22-24]. Thyristor inclusion in the TCSC module
enables it to have a smoother control of reactance against
to system parameter variations. In view of a huge power
system, TCSC implementation requires several such basic
compensators to be connected in series to obtain the
desired voltage rating and operating characteristics. It is
modeled as a controllable reactance, inserted in series
with the transmission line to adjust the line impedance
and thereby control the power flow.
Ii   jBii
Ij    jBji
  
jBij Vi 
 
jBjj 
 Vj 
(16)
For capacitive operation, we have
Bii = Bjj =
1
(17)
XTCSC
Bij = Bji = −
1
(18)
XTCSC
For inductive operation the signs are reversed
The active and reactive power equations at bus k are:
Pi = Vi Vj Bij sin( θi − θj )
(19)
Q i = −Vi2 Bii − Vi Vj Bij cos( θi − θj )
(20)
The series reactance regulates the amount of active power
flowing from bus i to bus j the change in reactance of
TCSC is
(i−1)
∆XTCSC = X iTCSC − XTCSC
(21)
The state variable XTCSC of the series controller is
updated based on optimization rules.
4.
Fig. 1: Basic TCSC model
In this paper, the reactance of the transmission line is
adjusted by TCSC directly. The TCSC is modeled as
variable impedance [25, 26]. It is shown in Fig.2. The
rating of TCSC depends on the reactance of the
transmission line where the TCSC is located:
Complex Power Flow Sensitivity
Index for Optimal Placement of
TCSC
A method based on the sensitivity of the sum of
variations of complex power flow in all lines with respect
to the change of reactance of a line is proposed. The
TCSC has been modelled as a variable series capacitive
reactance XTCSC, resulting in a decrease of the total line
reactance. The index is computed using Newton Raphson
power flow. CPSIj at a line j is given as:
𝑛𝑡𝑙
∆S n
CPSIj =
𝑛=1
∆X j
(22)
Where n=1, 2, 3,......., ntl and ntl = no.of transmission
lines.
∆Sn is change in complex power flow in line n
∆Xj is the reactance of the line j
Fig. 2: Block diagram of TCSC
Zij = R ij + Xij
(13)
Zline = R line + Xline
(14)
Xij = X line + XTCSC
(15)
Where XTCSC is reactance of TCSC, to avoid over
compensation, the working range of the TCSC is chosen
between -0.8Xline and 0.6Xline.
The transfer admittance matrix of the TCSC is given by
This index is calculated for all the lines. The minimum
and maximum values of CPSI are obtained. Normalized
complex power flow sensitivity index is defined as:
CPSInj =
CPSIj − CPSImin
CPSImax − CPSI min
(23)
Where CPSInj is the normalized complex power flow
sensitivity index at line j.
Highest positive normalized complex power flow
sensitivity index is the best location for placement of
TCSC.
3
Journal of Electrical Engineering
www.jee.ro
From the Tab. 1 it is observed that highest positive value
for CPSIn(j) is 1 for line no 7. So it is the best location
for placement of TCSC in the IEEE 14 bus system. From
the Tab. 2 it is observed that highest positive value for
CPSIn(j) is 1 for line no 9. So it is the best location for
placement of TCSC in the IEEE 30 bus system.
Tab.1: Complex power flow sensitivity indexes for all lines in the
IEEE 14 bus system.
Line
Line
CPSIn(j)
S. No
Line
CPSIn(j)
1
1-2
2
2-3
0.8331
11
4-9
0.4319
0
12
7-9
0.5345
3
4
2-4
0.4189
13
9-10
0.482
1-5
0.2641
14
6-11
0.4657
5
2-5
0.8747
15
6-12
0.4977
6
3-4
0.6675
16
6-13
0.4155
7
4-5
1
17
9-14
0.4727
8
5-6
0.3855
18
10-11
0.4722
9
4-7
0.5619
19
12-13
0.4832
10
7-8
0.4829
20
13-14
0.4759
.No
Tab.2: Complex power flow sensitivity indexes for all lines in the
IEEE 30 bus system.
Line
Optimal sizing of TCSC using the
Firefly Algorithm
The Firefly algorithm has been used to find the optimum
sizing of TCSC. It was developed by Dr Xin-She Yang at
Cambridge University in 2007. FA is based on natural
behaviour of the firefly, developed for solving the
multimodal optimization problem [27, 28]. Fireflies
called as lighting bugs, are one of the most special and
fascinating creatures in nature. For simplicity, the
following three ideal rules are introduced in FA
development those are 1) All the fireflies are gender-free
that is every firefly will attract the other firefly
substantive of their sex, 2) Attractiveness depend on their
brightness. The less bright one will move towards the
brighter one, 3) the landscape of the objective function
affects the firefly brightness. Let us consider the
continuous constrained optimization problem where the
task is to minimize multi objective function f(x). Firefly
algorithm is a dynamic converging algorithm. The
solution for the algorithm depends on the selection of
swarm size, maximum attractiveness value, the
absorption coefficient value and the iteration limit. The
basic steps of the FA can be summarized by the pseudo
code [29, 30].
Firefly Algorithm
Line
CPSIn(j)
S. No
Line
CPSIn(j)
1
1-2
0.4232
21
16-17
0.7326
2
1-3
0.7943
22
15-18
0.7082
3
2-4
0.7952
23
18-19
0.7266
4
3-4
0.8800
24
19-20
0.7576
5
2-5
0
25
10-20
0.6973
6
2-6
0.6968
26
10-17
0.7564
7
4-6
0.8331
27
10-21
0.7547
8
5-7
0.8282
28
10-22
0.5547
9
6-7
1.0000
29
21-22
0.9930
10
6-8
0.8254
30
15-23
0.5485
11
6-9
0.6773
31
22-24
0.4224
12
6-10
0.5921
32
23-24
0.5465
13
9-11
0.6805
33
24-25
0.6404
14
9-10
0.4868
34
25-26
0.6914
15
4-12
0.6793
35
25-27
0.6360
16
12-13
0.7023
36
28-27
0.5564
17
12-14
0.7236
37
27-29
0.6963
18
12-15
0.4829
38
27-30
0.6745
19
12-16
0.7365
39
29-30
0.6954
20
14-15
0.7215
40
8-28
0.7008
---
---
----
41
6-28
0.6973
.No
5.
………………………………………………..
Objective function f(x), x = (x1,…,xd)T
Generate initial population of fireflies xii ( i=1, 2…, n)
Light intensity Iii at xii is determined by f(xii)
Define light absorption coefficient γ
while ( t < MaxGeneration)
for ii = 1: n all n fireflies
for jj = 1: ii all n fireflies
if (Ijj > Iii), More firefly ii towards jj in d-dimension; end
if
Attractiveness varies with distance r
Evaluate new solutions and modify the light intensity
end for jj
end for ii
Rank all the fireflies and find the current best firefly
end while
Post process results and visualization
……………………………..
Pseudo code of the FA.
6.
Results and Discussion
In order to find the effectiveness of the proposed
Firefly Algorithm for Optimal Power Flow with TCSC,
the IEEE14, IEEE30 and IEEE 57 bus systems are taken.
An OPF program using Firefly algorithm is implemented
in MATLAB software without and with TCSC. The
results are presented and analysed. The input parameters
of Firefly Algorithm for the test system are given in the
Tab. 3.
4
Journal of Electrical Engineering
www.jee.ro
Tab.3: Input parameters of FA Algorithm
S.No
Tab.4: GENERATOR CHARACTERISTICS OF IEEE 14 BUS
SYSTEM
Parameters
Quantity
1
Number of fireflies
20
2
Max Generation
50
3
Alpha
(random
movement factor)
0.5
4
Beta (attractiveness
parameter)
0.5
5
Gama
(absorption
parameter)
a
Generator
BUS NO
In the IEEE 14 bus system bus no 1 is considered as a
slack bus and bus numbers 2,3,6,8 are considered as a PV
buses all other buses are considered as load buses. This
system has 20 interconnected lines. A MATLAB program
is written for the test system and the results have been
presented and analysed. Table. 4 indicates the generators
coefficients, minimum and maximum limit of real power
generation for generator buses.
Table. 5 indicates the voltage magnitudes in FA-OPF
without TCSC and FA-OPF with TCSC (By placing
TCSC at line No 7). The results indicate that there is a
good improvement in voltage profile with TCSC in
Firefly Algorithm based OPF.
The active power generation and power loss for the IEEE
14 bus test system without and with TCSC is shown in
Tab.6 and it is observed that active power losses are
reduced to 5.0631 MW from 5.4104 MW by placing
TCSC in Firefly Algorithm based Optimal Power Flow.
TCSC value was tuned to 0.0220 ohms using Firefly
Algorithm. In case of Genetic Algorithm based Optimal
Power Flow the TCSC value has been tuned to 0.031
ohms. Table. 7 represents the voltage deviation, TCSC
reactance value, total active power generation cost,
branch loading, FVSI for all lines, Objective function
value and active power losses for the IEEE 14 bus system
without TCSC and with TCSC using GA-OPF and FAOPF. The results clearly indicate the effectiveness of
Firefly Algorithm over Genetic Algorithm.
Table 8 & 9 indicates the FVSI values for Firefly
Algorithm based Optimal Power Flow without and with
TCSC with different reactive load conditions at bus
number 14. From these tables it can be inferred that
increase in reactive load would result in FVSI value to
unity leading to less line stability. By installing the TCSC
in Firefly Algorithm based Optimal Power Flow can
improve the FVSI that means line stability has been
improved.
($/MW
hr)
1
6.1. For 14 bus system
b
($/MW2/
Tab.5:
𝑷𝒎𝒂𝒙
𝑮
($/hr)
(MW)
(MW)
1
0.005
2.45
105
10
400
2
0.005
3.51
44.1
20
80
3
0.005
3.89
40.6
20
50
6
0.005
3.25
0
10
35
8
0.005
3
0
10
30
Comparison of bus voltages for 14 bus system using GA-OPF
and FA-OPF without and with TCSC
GA-OPF
BUS
No
/hr)
𝑷𝒎𝒊𝒏
𝑮
c
without
TCSC
GA-OPF with
TCSC
connected at
Line No 7
Voltage
FA-OPF
without
TCSC
FA-OPF with
TCSC
connected at
Line No 7
Voltage
(p.u)
Voltage (p.u)
(p.u)
Voltage (p.u)
1
1.06
1.06
1.06
1.06
2
1.045
1.045
1.045
1.045
3
0.9872
1.01
0.9925
1.01
4
1.0015
1.0287
1.0022
1.0267
5
1.0114
1.0378
1.0118
1.038
6
0.9813
1.07
0.9819
1.07
7
0.9817
1.0372
0.9829
1.0363
8
1.0218
1.09
1.0232
1.09
9
0.948
1.01
0.949
1.0089
10
0.9454
1.01
0.9464
1.0118
11
0.9591
1.032
0.9599
1.0367
12
0.9578
1.043
0.9584
1.0463
13
0.9458
1.0333
0.9465
1.0331
14
0.883
0.96
0.8839
0.9606
TCSC node
voltage
Tab.6:
1.0372
1.0347
Comparison of Real power loss for 14 bus system without
and with TCSC (TCSC placed at line number 7)
Parameter
Active Power
Generation in
MW
Reactive Power
Generation in
MVAR
Active Losses
in MW
Reactive
Losses in
MVAR
TCSC size
FA –OPF
without
TCSC
FA-OPF
with
TCSC
264.4104
264.0631
117.97
50
115.2766
113.3547
6.9251
6.4339
5.4104
5.0631
14.2728
11.468
5
8.8766
6.6128
---
0.031
----
0.0220
GA-OPF
with
out
TCSC
265.925
1
GAOPF
with
TCSC
265.43
39
120.672
8
5
Journal of Electrical Engineering
www.jee.ro
Tab.7: Comparison of objective function parameters before and after
installation of TCSC
Objective
function
parameters
Total Real
FA –OPF
without
TCSC
FA-OPF
with
TCSC
GA-OPF
with
out
TCSC
6.9251
GAOPF
with
TCSC
6.4339
5.4104
5.0631
0.5718
0.2819
0.5593
0.2773
Power Losses
Total Voltage
Deviation(p.u)
Branch loading
Fuel cost
FVSI for all
lines
Objective
function value
2.6532
2.6199
1280.32
1278.4
10
76
2.1963
1.7489
367.037
336.20
9
11
2.3502
2.3280
1206.3879
1105.2432
1.9871
1.6300
364.2483
333.6814
Tab.8: Comparison of FVSI by changing the reactive load at bus 14
before and after installation of TCSC
FVSI
(Q14=30
FVSI
MVAR)
MVAR)
FA –OPF
without
TCSC
0.0249
1
2
0.1277
0.06
0.1443
0.0599
3
0.0918
0.013
0.1242
0.0073
4
0.1176
0.0202
0.1455
0.0223
5
0.0772
0.0247
0.1074
0.0222
6
0.0071
0.0429
0.0101
0.0367
7
0.0204
0.0171
0.0235
0.0186
8
0.1116
0.1309
0.1686
0.1343
9
0.0751
0.038
0.1184
0.0274
10
FA-OPF
with
TCSC
0.0251
0.2213
0.1821
0.2395
11
0.1965
0.0651
0.2576
0.0888
12
0.1307
0.1011
0.1551
0.1144
13
0.0083
0.0144
0.0063
0.0214
14
0.0586
0.0998
0.0672
0.1152
15
0.0604
0.0589
0.0765
0.0712
16
0.1086
0.1091
0.1406
0.1339
17
0.2602
0.1847
0.3671
0.2572
18
0.0404
0.0879
0.0483
0.1051
19
0.0578
0.0603
0.0804
0.0785
20
0.2363
0.2551
0.3343
1.6299
2.5824
Total
0.175
FA-OPF
with
TCSC
0.0254
1.98
FVSI
FVSI
(Q14=60 MVAR)
(Q14=70 MVAR)
FA-OPF
with
TCSC
0.0228
FA –OPF
without
TCSC
0.2463
FA-OPF
with TCSC
1
FA-OPF
with
out TCSC
0.1017
2
0.1899
0.0673
77824.08
0.0247
0.0073
9758.097
0.0019
79.3714
0.0051
Line NO
3
0.207
0.028
0.0194
4
0.2769
5
0.1777
0.0146
4265.893
0.0119
6
0.0532
0.0309
0.3591
0.0143
7
0.0413
0.0235
2.6996
0.0196
8
0.3341
0.1467
4.5429
0.1834
9
0.2482
0.0046
0.686
0.0037
10
0.2145
0.2797
0.3403
0.3069
11
0.4383
0.23
0.1571
12
0.2409
0.1461
0.5752
0.1646
13
0.0019
0.0357
0.8769
0.0455
14
0.0951
0.1459
0.7784
0.1661
15
0.13
0.0418
0.1119
16
0.2462
0.1866
4.8691
0.2168
17
0.6884
0.4137
23.1054
0.4961
18
0.0747
0.1414
2.6273
0.1663
19
0.1561
0.1173
7586.467
0.1399
20
0.6324
0.4974
2.9831
0.5862
4.5485
2.5475
99558.87
2.8414
0.141
(Q14=40
FA-OPF
with
out TCSC
0.0257
Line NO
Tab.9: Comparison of FVSI by changing the reactive load at bus 14
before and after installation of TCSC
Total
0.097
From fig 3 it can be observed that by increasing the
reactive load at bus number 14, total FVSI value also
increases. Incorporating the TCSC in Firefly Algorithm
based Optimal Power Flow total FVSI value has been
reduced that indicates that line stability has been
improved.
0.335
1.914
6
Journal of Electrical Engineering
www.jee.ro
Tab.11: Comparison of bus voltages for 30 bus system using GA-OPF
and FA-OPF without and with TCSC
BUS
No
6.2. For 30 Bus System
In IEEE 30 bus system bus no 1 is considered as a
slack bus and bus no‟s 2,5,8,11,13 are considered as a PV
buses all other buses are considered as load buses. This
system has 41 interconnected lines. A MATLAB program
is coded for the test system and the results have been
tabulated. Table.10 represents the generators a
coefficient, minimum and maximum limits of real power
generation for generator buses.
Table.2 indicates that the optimal location for TCSC is
line no 9. By placing the TCSC at line no 9 in both
Genetic Algorithm and Firefly Algorithm based Optimal
Power Flows and the results have been presented.
Table.11 indicates the voltage magnitudes in FA-OPF
without TCSC and FA-OPF with TCSC (By placing
TCSC at line No 9). The results indicate that there is a
good improvement in voltage profile with TCSC in
Firefly Algorithm based OPF. The active power
generation and power loss for IEEE 30 bus test system
without and with TCSC is shown in Tab.12 and it is
observed that active power losses are reduced to 11.5926
MW from 12.5466 MW by placing TCSC in Firefly
Algorithm based Optimal Power Flow. TCSC value was
tuned to 0.0400 using Firefly Algorithm and for the same
the TCSC value has been tuned to 0.0468 using Genetic
Algorithm based Optimal Power Flow.
Tab.10: GENERATOR CHARACTERISTICS OF IEEE 30 BUS
SYSTEM
1
a
($/MW2/
hr)
0.00375
b
($/MW
/hr)
2
2
0.0175
5
Generator
BUS NO
c
($/hr)
𝑷𝒎𝒊𝒏
𝑮
(MW)
𝑷𝒎𝒂𝒙
𝑮
(MW)
0
50
300
1.75
0
20
80
0.0625
1
0
15
50
8
0.00834
3.25
0
10
35
11
0.025
3
0
10
30
13
0.025
3
0
12
40
FA-OPF
without
TCSC
FA-OPF with
TCSC
connected at
Line No 9
Voltage
(p.u)
Voltage (p.u)
Voltage
(p.u)
Voltage (p.u)
1.06
1.06
1.06
1.06
1
Fig. 3: Fig: 3 FVSI values for different reactive load conditions
GA-OPF with
TCSC
connected at
Line No 9
GA-OPF
without
TCSC
2
1.045
1.045
1.045
1.045
3
1.0145
1.0196
1.0196
1.0219
4
1.0044
1.0106
1.0107
1.0135
5
1.01
1.01
1.01
1.01
6
0.9981
1.0043
0.999
1.0056
7
0.9946
0.9988
0.995
0.9988
8
1.01
1.01
1.01
1.01
9
0.9647
0.991
0.9663
0.9912
10
0.908
0.9379
0.9093
0.9371
11
1.0427
1.082
1.0446
1.082
12
0.9461
0.9853
0.9532
0.9884
13
1.0085
1.071
1.0142
1.071
14
0.8874
0.9273
0.8944
0.9303
15
0.8917
0.9302
0.8974
0.9322
16
0.9218
0.9576
0.9262
0.9587
17
0.906
0.938
0.9082
0.9377
18
0.8832
0.9193
0.8873
0.9202
19
0.8819
0.9164
0.8851
0.9167
20
0.8875
0.9209
0.8902
0.9209
21
0.8735
0.9047
0.8751
0.904
22
0.8679
0.8993
0.8696
0.8986
23
0.8371
0.8741
0.8417
0.8754
24
0.7748
0.8095
0.7777
0.8097
25
0.8374
0.8624
0.8388
0.8621
26
0.8157
0.8414
0.8172
0.841
27
0.8883
0.9066
0.889
0.9062
28
0.9865
0.9928
0.9873
0.9938
29
0.865
0.8839
0.8657
0.8834
30
0.8516
TCSC node
Voltage
0.8708
0.8523
0.8703
0.9976
0.9989
Tab.12: Comparison of Real power loss for 30 bus test system without
and with TCSC (TCSC placed at line number 9)
Parameter
Active Power
Generation in
MW
Reactive Power
Generation in
MVAR
Active Losses in
MW
Reactive Losses
in MVAR
TCSC size
GA-OPF
with
out TCSC
GA-OPF
with
TCSC
FA –OPF
without
TCSC
FA-OPF
with
TCSC
300.1323
298.9865
295.9466
294.9926
256.8372
253.2349
239.7242
237.0999
16.7323
15.5865
12.5466
11.5926
51.9372
47.8382
34.8242
31.9679
------
0.0468
------
0.0400
7
Journal of Electrical Engineering
www.jee.ro
Tab.13: Comparison of objective function parameters before and after
installation of TCSC
Objective
GA-OPF
with
out
TCSC
function
parameters
Total Real
16.7323
Power Losses
Total Voltage
2.4521
GAOPF
with
TCSC
15.586
5
1.7663
FA –OPF
without
TCSC
12.5466
2.3984
FA-OPF
with
TCSC
11.5926
1.7642
Deviation(p.u)
Branch loading
Fuel cost
FVSI for all
lines
Objective
5.4414
5.4378
4.6713
1122.22
1118.1
1023.981
83
96
5
5.8644
5.243
5.6015
324.097
function value
0
322.32
312.9326
4.6066
1021.4473
5.1077
311.6005
Tab.14: Comparison of FVSI by changing the reactive load at bus 14
before and after installation of TCSC in IEEE 30 bus system
FVSI (Q14=20 MVAR)
26
0.0035
0.0073
0.0119
0.0051
27
28
0.1399
0.131
0.1477
0.1346
0.1679
0.1572
0.1776
0.1617
29
0.0313
0.0291
0.0335
0.0301
30
0.2451
0.2458
0.2401
0.2425
31
0.4728
0.4429
0.5016
0.4565
32
0.3157
0.3182
0.3068
0.3126
33
0.4662
0.381
0.5201
0.3961
34
0.0719
0.0681
0.0744
0.069
35
0.2959
0.2504
0.3228
0.258
36
0.3497
0.3135
0.3687
0.3192
37
0.0412
0.0396
0.0422
0.0399
38
0.0529
0.051
0.054
0.0513
39
0.0169
0.0162
0.0173
0.0164
40
0.0953
0.0683
0.107
0.0737
41
0.0412
0.0416
0.0421
0.0415
Total
5.6015
5.1076
6.2404
5.4621
Tab.15: Comparison of FVSI by changing the reactive load at bus 14
before and after installation of TCSC
FVSI (Q14=40
FVSI (Q14=30 MVAR)
FVSI (Q14=50 MVAR)
MVAR)
1
FA-OPF
with
out TCSC
0.0196
FA-OPF
with
TCSC
0.0234
FA –OPF
without
TCSC
0.0164
FA-OPF
with
TCSC
0.0208
2
0.1094
0.0934
0.1258
0.0949
3
0.1038
0.0783
0.126
0.0813
4
0.0238
0.0199
0.0278
5
0.0451
0.0492
6
0.0958
7
1
FA-OPF
with
out TCSC
0.0247
FA-OPF
with
TCSC
0.0314
FA –OPF
without
TCSC
3.5638
FA-OPF
with
TCSC
0.0599
2
0.1824
0.1074
0.0039
0.0495
3
0.1912
0.0892
0.2326
0.0897
0.0202
4
0.0422
0.0233
59484.73
0.0081
0.037
0.042
5
0.0396
0.0486
5.0783
0.0108
0.0929
0.0977
0.0914
6
0.2091
0.1001
0.8509
0.0728
0.039
0.0198
0.0215
0.0157
7
0.0736
0.0163
33.8875
0.0076
8
0.0719
0.058
0.0792
0.0617
8
0.149
0.0626
0.8762
0.0818
9
0.0101
0.0005
0.0152
0.002
9
0.0674
0.0027
19.3619
0.0154
10
0.0488
0.0192
0.0609
0.0252
10
0.0236
0.0276
0.0487
0.0538
11
0.1268
0.0567
0.1543
0.0614
11
0.2022
0.0731
0.032
0.0728
12
0.3215
0.2484
0.3596
0.2599
12
0.4291
0.2824
9.5571
0.2903
13
0.3564
0.4066
0.3642
0.4204
13
0.3963
0.4384
529.776
0.4597
14
0.2178
0.2025
0.2372
0.2121
14
0.2731
0.2243
1210.433
0.2374
15
0.2096
0.0929
0.2704
0.1163
15
0.3885
0.1492
0.082
0.1631
16
0.2774
0.3667
0.2927
0.4148
16
0.3257
0.4612
899.0658
0.5289
17
0.2317
0.2234
0.3244
0.303
17
0.4516
0.3815
6297.134
0.4707
18
0.1943
0.1962
0.2154
0.2169
18
0.2579
0.2339
12763.23
0.2598
19
0.0757
0.0945
0.0599
0.0907
19
0.0501
0.0798
44823.85
0.0767
20
0.0741
0.0556
0.1965
0.154
20
0.3748
0.2718
12.5555
0.407
21
0.0537
0.0738
0.0372
0.0699
21
0.0244
0.0585
0.2975
0.0552
22
0.0004
0.0166
0.0219
0.0053
22
0.0491
0.0123
1.216
0.0256
23
0.0074
0.0031
0.0213
0.004
23
0.0389
0.0149
0.0648
0.023
24
0.0188
0.0122
0.027
0.0163
24
0.0385
0.0224
3.0378
0.0271
25
0.0612
0.0426
0.0831
0.0537
25
0.1136
0.0705
0.8907
0.083
Line NO
Line NO
8
Journal of Electrical Engineering
www.jee.ro
Total
26
0.0207
0.0004
0.5833
0.0024
27
0.169
0.1383
0.0412
0.1436
28
0.2036
0.1664
0.0635
0.173
29
0.0393
0.0313
11.2937
0.0329
30
0.256
0.2325
3.196
0.2314
31
0.5752
0.4708
34.7376
0.491
32
0.3265
0.2979
0.2951
0.295
33
0.6558
0.4295
326.7163
0.4417
34
0.0846
0.0701
0.0046
0.0713
35
0.3939
0.2762
0.0093
0.2814
36
0.4197
0.3342
0.3417
0.3371
37
0.0472
0.0404
16.7764
0.0409
38
0.0599
0.0519
4835.505
0.0525
39
0.0194
0.0166
689.0327
0.0168
40
0.0896
0.0778
189.5542
0.098
41
0.0591
0.0432
1.0708
0.0384
7.8361
5.9609
132209.1
6.3771
6.3. For 57 Bus System
In IEEE 57 bus system, bus 1 is considered as slack bus
and buses 2,3,6,8,9,12 are considered as generator buses.
It consists of 50 load buses and 80 transmission lines.
From the Tab. 16 it is observed that highest positive value
for CPSIn(j) is 1 for line no76. So it is the best location
for placement of TCSC in the IEEE 57 bus system. After
placing the TCSC consider all the parameters of the
system, generation reallocation is carried out with a multi
objective function which is formed by considering the
cost of the real power generation, active power losses,
voltage deviation and branch loading. Results are
presented in Tab. 17 to 19.
Tab.16: Complex power flow sensitivity Index values for all lines in the
IEEE 57 bus system
S .No
1
2
From Fig 4 it has been observed that by incorporating the
TCSC in Firefly Algorithm based Optimal Power Flow
Real power losses were minimized. Table.13 represents
the voltage deviation, TCSC reactance value, total active
power generation cost and active power losses for IEEE
30 bus system without TCSC and with TCSC using GAOPF and FA-OPF. Table.14 & 15 indicates the FVSI
values for Firefly Algorithm based Optimal Power Flow
without and with TCSC at different reactive load
conditions at bus number 14. From this table it can be
observed that by increasing the reactive load FVSI values
reach towords one that indicates less line stability. By
installing the TCSC in Firefly Algorithm based Optimal
Power Flow can improve the FVSI that means line
stability has been improved.
3
4
5
6
CPSIn(j)
Line
No
S. No
CPSIn(j)
76
1
41
80
0.8837
36
0.9987
42
32
0.88
73
0.9986
43
17
0.8666
35
0.9982
44
58
0.863
46
0.9951
45
6
0.8616
31
0.9915
46
50
0.8593
7
44
0.991
47
68
0.8551
8
54
0.99
48
39
0.8506
9
29
0.9889
49
15
0.8426
10
19
0.9836
50
10
0.8324
11
74
43
0.9833
0.9804
51
52
14
2
0.832
0.8316
30
0.9759
53
26
0.8217
14
20
0.9755
54
47
0.8142
15
56
0.9733
55
59
0.8055
16
75
0.9679
56
24
0.8032
17
55
0.9675
57
65
0.7947
18
19
20
21
22
23
24
25
26
27
28
29
30
31
11
77
34
0.9582
0.9523
0.9514
58
59
60
22
60
41
0.794
0.7883
0.7746
38
69
70
64
42
0.951
0.945
0.9434
0.9412
0.9351
61
62
63
64
65
21
25
40
57
28
0.7716
0.7583
0.7499
0.7478
0.7311
16
67
66
27
78
7
0.9348
0.9291
0.9283
0.9244
0.9241
0.9219
66
67
68
69
70
71
48
18
8
79
37
52
0.7248
0.7194
0.7106
0.6948
0.6865
0.6816
32
9
0.9195
72
13
0.6612
12
13
Fig. 4: Fig: 4 comparisons of Real Power Losses
Line
No
9
Journal of Electrical Engineering
www.jee.ro
33
34
35
36
37
38
12
71
5
4
62
0.9141
0.9101
0.9079
0.8954
0.8922
73
74
75
76
77
63
0.8914
39
23
0.8909
40
72
0.8868
51
3
49
45
53
0.6058
0.5956
0.5916
0.5844
0.4902
78
1
0.4612
79
61
0.353
80
33
0
The results from Tab. 17 show that , for minimization of
the multi objective function, Firefly algorithm with
TCSC, the generation cost of the best solution is
46412.3565$/hr with 44.8432 MW line loss, 4.8530
voltage deviation and 12.7971 branch loading. The results
in Tab.17 indicate the values of the different parameters
of the multi objective function using Firefly algorithm
and genetic algorithm considering without & with TCSC.
From this table it is observed that Firefly algorithm gives
better results compared to genetic algorithm. Tab.18
shows that after placing the TCSC in the system voltage
profile has been improved. Tab. 19 shows the comparison
of FVSI before and after installation of TCSC in IEEE 57
bus system. From this table it is observed that by
incorporating the TCSC in the system improves the line
based stability.
Tab.17: Comparison of objective function parameters using GA and FAOPF considering without and with TCSC in IEEE 57 bus
system
Variables
Total real
power
generation
(MW)
Total real
power
generation
cost ($/hr)
Active
power Loss
(MW)
Voltage
deviation
(p.u)
Branch
loading (p.u)
FVSI value
for all lines
(p.u)
Reactance
of TCSC
(p.u)
Objective
function
value
GA-OPF
without
TCSC
1245.255
47701.16
49.4550
FA-OPF
without
TCSC
1241.847
46977.18
46.0472
GA OPF
with
TCSC at
line no 76
1244.255
47689.09
49.2455
FA- OPF
with
TCSC at
line no
76
1240.643
46412.35
44.8432
5.9295
5.7421
4.9056
4.8530
13.8480
13.3127
14.1600
12.7971
7.9431
7.6171
7.5205
7.3326
----
0.4201
---11942.59
11760.57
11939.35
Tab.18: Comparison of bus voltages for 57 bus system using FA-OPF
without and with TCSC
Voltage
(p.u)
FA-OPF
with
TCSC at
Line No
76
Voltage
(p.u)
31
0.7224
0.8143
1.01
32
0.7406
0.8589
1
33
0.7376
0.8563
1.0017
0.9941
34
0.7888
0.9255
5
0.997
0.9945
35
0.7978
0.9362
6
1
1
36
0.8099
0.9485
7
0.985
0.9879
37
0.8201
0.9605
8
1.005
1.005
38
0.852
1
9
0.9902
1
39
0.8177
0.9569
10
0.9801
0.9979
40
0.8075
0.9443
11
0.9591
0.9831
41
0.8186
0.877
12
1.015
1.015
42
0.7778
0.8535
13
0.9706
0.9974
43
0.9191
0.9526
14
0.9445
0.9907
44
0.884
1.0033
15
1.0073
1.0167
45
0.964
1.023
16
1.0136
1.0142
46
0.9149
0.993
17
1.0186
1.0193
47
0.8797
0.9882
18
0.9625
0.9594
48
0.8732
0.9916
19
0.9005
0.9109
49
0.8943
0.9879
20
0.8754
0.8943
50
0.8982
0.9696
21
0.8542
0.8884
51
0.9633
0.9922
22
0.8508
0.8872
52
0.9244
0.9321
23
0.8498
0.8862
53
0.909
0.9171
24
0.85
0.8854
54
0.9385
0.947
25
0.7826
0.8419
55
0.9775
0.9864
26
0.8554
0.8885
56
0.7745
0.8645
27
0.9143
0.9312
57
0.7693
0.8698
28
0.9435
0.9542
29
0.9662
0.973
30
0.757
0.8264
FAOPF
without
TCSC
FA-OPF
with TCSC
at Line No
76
Voltage
(p.u)
Voltage
(p.u)
1
1.04
1.04
2
1.0334
3
1.0115
4
BUS
No
FA-OPF
without
TCSC
Tab.19: Comparison of FVSI before and after installation of TCSC in
IEEE 57 bus system
Line
No
FVSI
without
TCSC
FVSI with
TCSC at
Line No
76
1
0.0432
0.1334
2
0.0756
3
4
FVSI
without
TCSC
FVSI with
TCSC at
Line No 76
41
0.0715
0.0573
0.0256
42
0.0828
0.0718
0.0247
0.0156
43
0.1156
0.095
0.0134
0.0059
44
0.052
0.0653
5
0.0145
0.0047
45
0.0109
0.0099
6
0.0696
0.0556
46
0.204
0.1991
7
0.0335
0.0276
47
0.0312
0.0292
8
0.0097
0.039
48
0.0409
0.0378
0.3111
11618.96
BUS
No
Line
No
10
Journal of Electrical Engineering
www.jee.ro
9
0.0299
0.0122
49
0.036
0.036
10
0.081
0.0757
50
0.1163
0.1184
0.0107
11
0.1591
0.1115
51
0.0096
12
0.0152
0.016
52
0.0093
0.0115
13
0.0882
0.0702
53
0.0002
0.0106
14
0.0826
0.0371
54
0.4858
0.4548
15
0.1165
0.1133
55
0.1007
0.0782
16
0.0247
0.0259
56
0.562
0.5083
17
0.0072
0.0067
57
0.13
0.0778
18
0.01
0.0595
58
0.1596
0.1094
19
0.1369
0.121
59
0.12
0.0914
20
0.1395
0.1236
60
0.1249
0.0933
21
0.0023
0.0063
61
0.0441
0.0279
22
0.0467
0.0388
62
0.119
0.0467
23
0.1517
0.1232
63
0.0432
0.0251
24
0.074
0.0676
64
0.2567
0.2195
25
0.2172
0.1782
65
0.0657
0.0589
26
0.0202
0.0207
66
0.2823
0.1699
27
0.0458
0.0466
67
0.1017
0.089
28
0.0878
0.0837
68
0.041
0.0338
29
0.1755
0.101
69
0.0874
0.1025
30
0.1032
0.0501
70
0.1082
0.1204
31
0.1014
0.0268
71
0.1587
0.1475
32
0.0207
0.0056
72
0.3095
0.1987
33
0.0026
0.0062
73
0.1506
0.1911
34
0.0144
0.0759
74
0.0272
0.0267
35
0.261
0.2361
75
0.0141
0.0329
36
0.261
0.2361
76
0.2117
0.24
37
0.026
0.0147
77
0.0144
0.028
38
0.2183
0.129
78
0.2596
0.1194
39
0.0805
0.0517
79
0.1328
0.0721
40
0.0615
0.0437
80
0.0493
0.0526
effectiveness of the proposed approach. The obtained
results show that TCSC is the most effective series
compensation device that can significantly increase the
line stability of the power system.
References
[1]
P. Kundur, Power System Stability and Control. New
York: McGraw-Hill, Inc., 1993.
[2]
G W Stagg and A H El-Abid, „Computer Methods in
Power System Analysis‟(Book), McGraw-Hill Book Co,
1968.
[3]
N. G. Hingorani and L. Gyugyi, “Understanding
FACTS: Concepts and Technology of Flexible AC
Transmission System”, IEEE Press, 2000.
[4]
Camacho Yuryevich Janson, Wong Po kit. Evolutionary
programming based optimal power flow algorithm.
IEEE Trans Power System 1999;14(4): 1245–50.
[5]
Varaprasad Janamala, Chandra Sekhar Koritala,“
OPTIMAL
LOCATION
OF
UPFC
FOR
CONGESTION RELIEF IN DEREGULATED POWER
SYSTEMS”, Journal of Electrical Engineering, pp.1-8,
2014.
[6]
Sung-Hwan Song, Jung-Uk Lim, Seung-Il Moon,
“FACTS operation scheme for enhancement of power
system security,” in Proc. 2003 IEEE Bologna Power
Tech Conference, Vol. 3, pp. 36-41, June 2003.
[7]
Canizares C A and Faur Z T (1999), “Analysis of SVC
and TCSC Controllers in Voltage Collapse”, IEEE
Trans. on Power Systems, Vol. 14, No. 1, pp. 158-165.
[8]
Yunqiang Lu, Ali Abur, “Static security enhancement
via optimal utilization of Thyristor-Controlled Series
Capacitors,” IEEE Trans. Power System., vol.17,
pp.324-329, May 2002.
[9]
R. benabid, M. Boudour, M.A. Abido, “ Optimal
location and setting of SVC and TCSC devices using
nondomonated sorting particle swarm optimization”,
Electric Power Systems Research 79, 1668-1677, July
2009.
[10]
TLIJANI Kamel , GUESMI Tawfik , HADJ ABDALLAH
Hsan and OUALI Abderrazak, “ 0ptimal location and
parameter setting of TCSC based on Sensitivity
analysis”, 2012 First international conference on
renewable energies and vehicular technology (IEEE
conference), pp. 420-424.
[11]
P. P. Narayana, M. A. Abdel Moamen, and B.J. Praveen
Kumar “ Optimal location and initial parameter settings
of multiple TCSCs for reactive power planning using
genetic algorithm”, IEEE Power Engineering Society
General Meeting, Vol.1, pp. 1110 – 1114, 6-10 June
2004.
[12]
Carpentier. J “Optimal Power Flows”, Electrical Power
and Energy Systems, Vol.1, April 1979, pp 959-972.
[13]
Bakirtzis AG, Biskas PN, Zournas CE, Petridis V.
Optimal power flow by enhanced genetic algorithm.
IEEE Trans Power Syst 2002;17(2):229–36.
[14]
Ying Xiao, Y.H. Song and Y.Z. Sun, “Power flow
7. Conclusion
In this paper, Sensitivity Analysis based Complex
Power Flow Sensitivity Index (CPSI) has been
implemented for optimal location of TCSC. After placing
the TCSC in best location, a new swarm based Firefly
Algorithm has been presented to solve the optimal sizing
of TCSC. The effectiveness of Firefly Algorithm was
presented. The results show that incorporating the TCSC
in the IEEE 14, IEEE 30 and IEEE57 bus systems can
reduce the total active power losses, improve the voltage
profile of the system and enhance the line stability. For
finding the best size of a TCSC, Firefly Algorithm based
optimization technique, with the objective of reducing
total generation cost, voltage deviation, active power
losses and branch loading were implemented. The
comparative study of the Firefly Algorithm based
Optimal Power Flow with GA based Optimal Power Flow
in solving the optimal tuning problem also reflected the
11
Journal of Electrical Engineering
www.jee.ro
control approach to power systems with embedded
FCATS devices”,IEEE transaction on power systems,
vol,17, No.4 ,Nov. 2002, pp. 943 – 950.
[15]
Gerbex R Cherkaoui and Germond A J (2001), “Optimal
Location of Multi-Type FACTS Devices in a Power
System by Means of Genetic Algorithms”, IEEE
Transaction Power Systems, Vol. 16, August, pp. 537544.
[16]
T. Mirko, R. Dragoslav, "An initialization procedure in
solving optimal power flow by genetic algorithm",
IEEE Transactionson Power Systems, 2006, vol. 21, pp.
480-7.
[17]
P. Pezzini, O.G. Bellmunt, and A. S. Andrue,
“Optimization Techniques to improve energy efficiency
in power system,” International Journal Renewable and
Sustainable Energy 2011, 2028-2041.
[18]
Acha E., Fuerte-Esquivel C, Ambriz-Perez H and
Angeles C., “FACTS: Modelling and Simulation in
Power Networks”. John Wiley & Sons, 2004.
[19]
D. Radu, and Y. Besanger, “ A multi-objective genetic
algorithm approach to optimal allocation of multi-type
FACTS devices for power system security,” IEEE
Power Engineering Society General Meeting, pp. 8, 1822 June 2006.
[20]
Fuerte-Esquivel C , Acha E., Ambriz-Perez H., “A
Thyristor Controlled Series Compensator Model for the
Power Flow Solution of Practical Power Networks”
IEEE Trans on Power Systems, Vol. 15, N0.1, pp.129136, February 2000.
[21]
Wei Shao, Vittal, V., “LP-Based OPF for Corrective
FACTS Control to Relieve Overloads and Voltage
Violations”, IEEE Trans. Power Syst. Vol. 21, No. 4,
pp.1832-1839, Nov. 2006.
[22]
Srinivasa Rao Pudi, S.C. Srivastava, “Optimal
Placement of TCSC Based on a Sensitivity Approach for
Congestion Management”, in Proc. of Fifteenth
National Power Systems Conference (NPSC), IIT
Bombay, December 2008, pp. 558-563, Dec. 2008.
[23]
Ambriz-Pérez H., Acha E., Fuerte-Esquivel CR
“TCSC-firing angle model for optimal power flow
solutions using Newton's method”, International Journal
of Electrical Power & Energy Systems, Volume 28,
Issue 2, February 2006, Pages 77-85.
[24]
Shenghu Li “Power Flow Control Effect with TCSC on
Operation Margin of Zone 3 Impedance Relays”
International Journal of Electrical Power & Energy
Systems, Vol. 32, No. 9, pp. 998-1004, November 2010.
[25]
Tinney W. F., Hart C. E., “Power Flow Solution by
Newton‟s Method”, IEEE Transactions on Power
Apparatus and Systems, Vol. PAS-86, No.11, pp. 18661876, November 1967.
[26]
N P Padhy and Abdel-Moamen M. A., “Power Flow
Control and Solutions with Multiple and Multi-Type
FACTS Devices” Electric Power Systems Research,
Vol. 74, pp. 341-351, June 2005.
[27]
X.-S. Yang,
"Firefly
algorithms
for
multimodal
optimization," Stochastic Algorithms: Foundation and
Applications SAGA 2009, vol.5792, pp. 169-178, 2009.
[28]
X. S. Yang, “Firefly algorithm, Levy flights and global
optimization,” in Research and Development in
Intelligent Systems XXVI, pp. 209–218, Springer,
London, UK, 2010.
[29]
X. S. Yang, Nature-Inspired Meta-Heuristic Algorithms,
Luniver Press, Beckington, UK, 2008.
[30]
S. Lukasik and S. Zak, “Firefly algorithm for continuous constrained optimization tasks,” in Proceedings
of the International Conference on Computer and
Computational Intelligence (ICCCI ‟09), pp. 97–106,
Springer, Wroclaw, Poland, October 2009.
About Authors
Author-Venkateswara Rao BATHINA was born in
Ramabhadrapuram, Andhra Pradesh, India in 1978. He
received his Bachelor degree in Electrical and Electronics
Engineering from College of Engineering, Gandhi
Institute of Technology And Management (GITAM),
Visakhapatnam, India in 2000, and the Master degree in
Electrical Power Engineering from the College of
Engineering, JNTU, Hyderabad in 2007. He received his
Doctoral degree from Jawaharlal Nehru Technological
University, Hyderabad. He is presently working as
Assistant Professor in the Department of Electrical and
Electronics
Engineering,
GITAM
University,
Visakhapatnam. His research interests are Power system
stability analysis, FACTS devices, Power system control
and optimization. He has published several research
papers in national, international conferences and journals.
Co-author-Venkata Nagesh Kumar GUNDAVARAPU
was born in Visakhapatnam, India in 1977. He graduated
College of Engineering, Gandhi Institute of Technology
and Management, Visakhapatnam, India, Masters Degree
from the College of Engineering, Andhra University,
Visakhapatnam. He received his Doctoral degree from
Jawaharlal Nehru Technological University, Hyderabad.
He is presently working as Associate Professor in the
Department of Electrical and Electronics Engineering,
GITAM University, Visakhapatnam. His research
interests include gas insulated substations, FACTS
devices, Power System Stability analysis, fuzzy logic and
neural network applications, distributed generation,
Partial Discharge Studies and Bearing less drives. He has
published several research papers in national and
international conferences and journals. He received
“Sastra Award” , “Best Paper Award” and “Best
Researcher Award”. He is a member of various societies,
ISTE, IEEE, IE and System Society of India. He is also a
reviewer for IEEE Transactions on Dielectrics and
Electrical Insulation, Power Systems and a member on
Board of several conferences and journals.
12